University of Virginia Mathematical Physics Seminar 2009-10

September 9 Ira Herbst (UVa)
The Navier-Stokes Equations, I : Introductory Ideas
September 16 Ira Herbst (UVa)
The Navier-Stokes Equations, II : Critical Spaces, Relevant Sobolev Inequalities
September 23 Ira Herbst (UVa)
The Navier - Stokes equations, III: Existence, analyticity
September 30 Ira Herbst (UVa)
The Navier - Stokes equations IV: The analyticity radius
October 14 John Imbrie (UVa)
Random walks, Markov chains, and Gaussian integrals.
October 21 John Imbrie (UVa)
Self-avoiding walk and fermionic gaussian integrals
October 28 John Imbrie (UVa)
Renormalization group for the hierarchical self-avoiding walk
November 4 John Imbrie (UVa)
The broken supersymmetry phase of  self-avoiding walk
November 11 Pierluigi Falco (IAS Princeton)
The exact solution of the two dimensional Ising model
Many different methods have been designed for deriving the exact solution of the 2D Ising model. I will review in details how the combinatoric approach gives us the Onsager's formula of the free energy  and, time permitting,  the Wu's formula of the spin-spin correlation. This method is important since, as I will discuss in the following week's  talk,  it allows us to find rigorous results on Ising-like models without an exact solution.
[ref.: C.J. Thompson, "Mathematical Statistical Mechanics", ch.6; and T.Spencer , Phys. A 279 (2000)]
November 18 Pierluigi Falco (IAS Princeton)
The Kadanoff's formulas for the Eight-Vertex and the Ashkin-Teller models
In 1977 Kadanoff conjectured two "extended" scaling formulas for two classical, Ising-like, planar systems: the Eight-Vertex and the Ashkin-Teller models. After introducing the models, I will discuss how the use of the Grassmann variables  and the rigorous renormalization group allows us to prove one of the two.
[ref.: G.Benfatto, P.Falco, V.Mastropietro , CMP 292 (2009)]
December 2 Ajay Chandra (UVa)
Non-Gaussian fixed points for the block spin transformation on the hierarchical phi-4 model
December 7 Ajay Chandra (UVa)--2:30pm Monday, Note different day and time
Non-Gaussian fixed points for the block spin transformation on the hierarchical phi-4 model, cont.
December 16 Ajay Chandra (UVa)
Non-Gaussian fixed points for the block spin transformation on the hierarchical phi-4 model, cont.
January 27 Ajay Chandra (UVa)
Non-Gaussian fixed points for the block spin transformation on the hierarchical phi-4 model, cont.
February 3 Ajay Chandra (UVa)
Non-Gaussian fixed points for the block spin transformation on the hierarchical phi-4 model, cont.
February 10 Ira Herbst (UVa)
Existence and non-existence of ground states in some infrared singular field theory models
February 17 Ira Herbst (UVa)
Existence and non-existence of ground states in some infrared singular field theory models, cont.
February 24 Ira Herbst (UVa)
Existence and non-existence of ground states in some infrared singular field theory models, cont.
March 17 Abdelmalek Abdesselam (UVa)
Anderson localization in a supersymmetric model (after M. Disertori and T. Spencer)
March 24 Abdelmalek Abdesselam (UVa)
Anderson localization in a supersymmetric model (after M. Disertori and T. Spencer), cont.
March 31 David Hasler (William and Mary)
On the AC spectrum of one-dimensional random Schroedinger operators with matrix-valued potentials
April 7 Larry Thomas (UVa)
Stability of Polarons
April 14 Larry Thomas (UVa)
Stability of Polarons, cont.
April 16* Margherita Disertori (Université de Rouen)--2:00pm Friday, Note different day
A supersymmetric model for quantum diffusion in 3d
We consider a lattice field model which qualitatively reflects the phenomenon of Anderson localization and delocalization for real symmetric band matrices. We prove that in three or more dimensions the model has a `diffusive' phase at low temperatures. For the same model localization at high temperatures was proved for any dimension d ≥ 1. Our analysis uses estimates on non-uniformly elliptic Green's functions and a family of Ward identities coming from internal supersymmetry (joint work with T. Spencer and M. Zirnbauer).
April 21 Razvan Gurau (Perimeter Institute, Waterloo)
Introduction to Group Field Theory
Group field theory is the higher-dimensional generalization of random matrix models. As it has built-in scales and automatically sums over metrics and discretizations, it provides a combinatoric origin for space time. Its graphs facilitate an approach to algebraic topology which I exemplify by introducing a graph’s cellular structure and associated homology.
April 28 Razvan Gurau (Perimeter Institute, Waterloo)
Amplitudes in Group Field Theory
In this talk I detail the relation between the Feynman amplitudes of graphs in Group Field Theory and the fundamental group. I then propose a generalization of the notion of planarity to Group Field Theory and compute the amplitude of generalized planar graphs.
March 24 Abdelmalek Abdesselam (UVa)
Anderson localization in a supersymmetric model (after M. Disertori and T. Spencer), cont.

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Contact:
John Imbrie